The Cauchy Operator for Basic Hypergeometric Series

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator $T(bD_q)$. Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the $q$-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big $q$-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic

Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

High Resolution Chandra Spectroscopy of Gamma Cassiopeia (B0.5IVe)

gamma Cas has long been famous for its unique hard X-ray characteristics. We report herein on a 53 ks Chandra HETGS observation of this target. An inspection of our spectrum shows that it is quite atypical for a massive star, with abnormally weak Fe XXV, XXVI lines, Ly-alpha lines of H-like species from Fe XVII, XXIII, XXIV, S XVI, Si XIV, Mg XII, Ne X, O VII, VIII, and N VII. Also, line ratios of the rif-triplet of for a few He-like ions XVII are consistent with the dominance of collisional atomic processes. Yet, the presence of Fe and Si fluorescence K features indicates that photoionization also occurs in nearby cold gas. The line profiles indicate a mean velocity at rest and a broadening of 500 km/s. A global fitting analysis of the line and continuum spectrum finds that there are 3-4 plasma emission components. The dominant hot (12 keV) component and has a Fe abundance of 0.22 solar. Some fraction of this component (10-30%) is heavily absorbed. The other 2-3 components, with temperatures 0.1, 0.4, 3 keV, are "warm," have a nearly solar composition, a lower column absorption, and are responsible for most other emission lines. The strength of the fluorescence features and the dual-column absorption model for the hot plasma component suggest the presence near the hot sites of a cold gas structure with a column density of 10^23 cm^-2. Since this value is consistent with theoretical estimates of the vertical disk column of this star, these attributes suggest that the X-rays originate near the star or disk. It is possible that the Fe anomaly in the hot component is related to the First Ionization Potential effect found in coronal structures around active cool stars. This would be yet another indication that the X-rays -rays are produced in the immediate vicinity of the Be star.Comment: 32 pages, 4 figures (Fig. 3 colorized.) To be published in 01/10/04 Astrophysical Journal, Main Journal; included figures and updated formattin

A New Calculation of Ne IX Line Diagnostics

We describe the effect that new atomic calculations, including fully-relativistic R-matrix calculations of collisional excitation rates and level-specific dielectronic and radiative recombination rates, have on line ratios from the astrophysically significant ion Ne IX. The new excitation rates systematically change some predicted Ne IX line ratios by 25% at temperatures at or below the temperature of maximum emissivity (4x10^6 K), while the new recombination rates lead to systematic changes at higher temperatures. The new line ratios are shown to agree with observations of Capella and sigma^2 CrB significantly better than older line ratios, showing that 25-30% accuracy in atomic rates is inadequate for high-resolution X-ray observations from existing spectrometers.Comment: 5 pages, 6 figure

International Coercion, Emulation and Policy Diffusion: Market-Oriented Infrastructure Reforms, 1977-1999

Why do some countries adopt market-oriented reforms such as deregulation, privatization and liberalization of competition in their infrastructure industries while others do not? Why did the pace of adoption accelerate in the 1990s? Building on neo-institutional theory in sociology, we argue that the domestic adoption of market-oriented reforms is strongly influenced by international pressures of coercion and emulation. We find robust support for these arguments with an event-history analysis of the determinants of reform in the telecommunications and electricity sectors of as many as 205 countries and territories between 1977 and 1999. Our results also suggest that the coercive effect of multilateral lending from the IMF, the World Bank or Regional Development Banks is increasing over time, a finding that is consistent with anecdotal evidence that multilateral organizations have broadened the scope of the “conditionality” terms specifying market-oriented reforms imposed on borrowing countries. We discuss the possibility that, by pressuring countries into policy reform, cross-national coercion and emulation may not produce ideal outcomes.http://deepblue.lib.umich.edu/bitstream/2027.42/40099/3/wp713.pd

CRPV Genomes with Synonymous Codon Optimizations in the CRPV E7 Gene Show Phenotypic Differences in Growth and Altered Immunity upon E7 Vaccination

Papillomaviruses use rare codons relative to their hosts. Recent studies have demonstrated that synonymous codon changes in viral genes can lead to increased protein production when the codons are matched to those of cells in which the protein is being expressed. We theorized that the immunogenicity of the virus would be enhanced by matching codons of selected viral genes to those of the host. We report here that synonymous codon changes in the E7 oncogene are tolerated in the context of the cottontail rabbit papillomavirus (CRPV) genome. Papilloma growth rates differ depending upon the changes made indicating that synonymous codons are not necessarily neutral. Immunization with wild type E7 DNA yielded significant protection from subsequent challenge by both wild type and codon-modified genomes. The reduction in growth was most dramatic with the genome containing the greatest number of synonymous codon changes